Number of integers in n-th generation of tree T(-1/3) defined in Comments.

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =2a(5) =2a(6) =3a(7) =5a(8) =6a(9) =8a(10) =12a(11) =17a(12) =23a(13) =32a(14) =44a(15) =61a(16) =86a(17) =119a(18) =164a(19) =228a(20) =318a(21) =442a(22) =614a(23) =850a(24) =1181a(25) =1643a(26) =2282a(27) =3167a(28) =4398a(29) =6110